Fabry-Perot Interferometry at the =2/5 Fractional Quantum Hall State

Electronic Fabry-Perot interferometry is a powerful method to probe quasiparticle charge and anyonic braiding statistics in the fractional quantum Hall regime. We extend this technique to the hierarchy v = 2/5 fractional quantum Hall state, possessing two edge modes that in our device can be interfered independently. The outer edge mode exhibits interference similar to the behavior observed at the v = 1/3 state, indicating that the outer edge mode at v = 2/5 has properties similar to the single mode at v = 1/3. The inner mode shows an oscillation pattern with a series of discrete phase jumps indicative of distinct anyonic braiding statistics. After taking into account the impact of bulk-edge coupling, we extract an interfering quasiparticle charge e* = 0.17 +/- 0.02 and anyonic braiding phase Oa = (-0.43 +/- 0.05) x 2x-, which serve as experimental verification of the theoretically predicted values of e* = 51 and Oa =-(4x-/5).